
import pandas as pd
import numpy as np
import random
import yfinance as yf

import matplotlib.pyplot as plt
import seaborn as sns
import plotly.express as px
from plotly.subplots import make_subplots
import plotly
plotly.offline.init_notebook_mode(connected=True)

from sklearn.preprocessing import StandardScaler
from sklearn.decomposition import PCA
from sklearn.cluster import KMeans
from scipy.cluster.hierarchy import fcluster,linkage, dendrogram, leaves_list


### GET S&P 500 constituents from Wikipedia ###
def get_sp500_cons():
    '''
    Extract S&P 500 companies from wikipedia and store tickers and Sectors / Industries as df
    Returns a df of tickers, name, sectors, and industries
    '''
    URL = 'https://en.wikipedia.org/wiki/List_of_S%26P_500_companies'
    df = pd.read_html(URL)[0]
    df['Symbol'] = df['Symbol'].str.replace('.','-')
    df = df.drop(['Headquarters Location','Date added','CIK','Founded'],axis=1)
    df = df.sort_values(by=['GICS Sector','GICS Sub-Industry'])
    df = df.set_index('Symbol')
    df.dropna(inplace=True)
    return df


# Tickers scrapping
data = get_sp500_cons()
data.head()

/var/folders/sr/2_q1kwss0cg7rt_ny655psg80000gn/T/ipykernel_8565/3925123783.py:9: FutureWarning:

The default value of regex will change from True to False in a future version. In addition, single character regular expressions will *not* be treated as literal strings when regex=True.


### GET prices from yfinance ###
def get_prices(tickers,start='1995-12-31'):
    '''
    Dowload prices from yfinance from a list of tickers. 
    Returns a df of daily prices
    '''
    prices  = yf.download(tickers, start=start,interval='1d',)
    prices = prices['Adj Close']
    # fwd fill last prices for missing daily prices
    prices = prices.asfreq('D').ffill()
    return prices


# Collect prices from yfinance into stock_data df
ticker_list = data.index.to_list()
start_date = '2015-01-01'
stock_data = get_prices(tickers=ticker_list,start=start_date)

[*********************100%***********************]  503 of 503 completed


stock_data.head()


### COMPUTE Returns on specified frequency ###
def get_returns(prices_df,freq='D'):
    '''
    Input daily prices df of prices. Use freq as 'D','B', 'W', or 'M' for daily, business, weekly, or monthly.
    Output returns_df in selected frequency
    '''
    prices_d = prices_df.dropna(axis=0,how='all')
    prices_d = prices_d.dropna(axis=1)
    prices_res = prices_d.resample(freq).last()
    prices_res = prices_res.dropna(axis=1)
    returns = prices_res.pct_change().dropna()
    return returns


# Set Frequency of returns
freq = 'W'
# Compute returns
returns = get_returns(stock_data,freq=freq)
returns.head(3)


### SAMPLE N stocks => returns_df ###
def get_sample(returns,N=returns.shape[1]):
    '''
    Sample N stocks randomly from stocks in returns df columns
    Return a returns_df of random sampled stocks
    '''
    sample = random.sample(returns.columns.to_list(),N)
    return returns[sample]


# Sample N stocks
returns_df = get_sample(returns,N=350)
returns_df.head(3)


### RUN PCA ###
def train_PCA(returns, n_comp=20):
    """
    From returns df, compute n_comp PCA and returns W,pca,X_proj,cum_var
    """
    # Set X
    X = returns
    # Standardize returns into X_scal
    scaler = StandardScaler()
    scaler.fit(X)
    X_scal = pd.DataFrame(scaler.transform(X), columns=X.columns, index=X.index) 
    # Run PCA
    pca = PCA(n_comp)
    pca.fit(X_scal)
    # Get PCA loadings
    W = pca.components_
    W = pd.DataFrame(W.T,
                     index=X.columns,
                     columns=pca.get_feature_names_out())
    # Print cum explained variance by n_comp components
    cum_var = np.cumsum(pca.explained_variance_ratio_)
    print(f'Total explained variance:{np.round(cum_var.max(),2)} with {n_comp} PCs')
    
    X_proj = pca.transform(X_scal)
    X_proj = pd.DataFrame(X_proj, columns=pca.get_feature_names_out(),index=X_scal.index)
    
    return W,pca,X_proj,cum_var


# Run PCA on returns df 
W,pca,X_proj,cum_var = train_PCA(returns_df,n_comp=20)

# Plot total cumulative explained variance using n_comp PCs
import plotly
plotly.offline.init_notebook_mode(connected=True)
fig = px.bar(cum_var,
              width=800,
             height=600,
              title='Cumulative Variance explained by PCs',
            )
fig.update_layout(xaxis_title='PCs', yaxis_title='Cum Var',showlegend=False,)
fig.show()

Total explained variance:0.67 with 20 PCs


# Quick Viz of PC orthogonality
plt.figure(figsize=(12,8))
sns.heatmap(X_proj.corr(), cmap='coolwarm')
plt.title('Correlation Heatmap - Princpal Components')
plt.show()


# Plot PC0 vs PC1 - Use Sectors as colors
df = W.join(data[['Security','GICS Sector']])
fig = px.scatter(df, x='pca0', y='pca1',
                    title='PCA - PC1 vs PC2',
                    color='GICS Sector',
                 width=1000,
                 height=700,
                    hover_data=[df.index,df.Security],
               )

fig.show()


# Plot top 3 PCs
fig = px.scatter_3d(df, x='pca0', y='pca1', z='pca2',
                    title='PCA - Top 3 PCs',
                    width=1000,
                    height=700,
                    color='GICS Sector',
                    hover_data=[df.index,df.Security],
                   )

fig.show()


### GET K-Means clusters labels based on PCA ###
def get_kmeans_clusters(W,k=11):
    """
    From W matrix of PCA loadings for each stock, 
    train K-Means to cluster stocks in k clusters.
    Returns clusters labels assigned to each stock in a df
    """
    kmeans = KMeans(n_clusters=k)
    kmeans.fit(W)
    labels = kmeans.labels_
    # Assign stocks to clusters
    clusters_k = pd.DataFrame(labels,index=W.index,columns=['cluster'])
    clusters_k = clusters_k.sort_values(by='cluster')
    return clusters_k


# Set number of clusters
k = 11 # in-line with GICS Sector classification

# PCA + K-Means cluster labels
clusters_k = get_kmeans_clusters(W,k=k)


### RUN  HCA ###
def get_hca_clusters(X,k=returns_df.shape[1]/10):
    """
    From X returns_df compute Z linkage matrix on C cov Matrix, 
    use fcluster to split linkage matrix into k clusters
    Returns k clusters labels assigned to each stock in a df
    """
    # Build Covariance Matrix C
    C = X.cov()

    # Compute the linkage matrix using Ward's method
    Z = linkage(C, method='ward', metric='euclidean')

    # Use the fcluster function to split the dendogram into k clusters
    labels = fcluster(Z, k, criterion='maxclust')

    # Assign cluster labels to stocks 
    clusters_h = pd.DataFrame(labels,index=X.columns,columns=['cluster'])
    clusters_h = clusters_h.sort_values(by='cluster')
    return clusters_h, Z


# Set number of clusters
k = 11 # in-line with GICS Sector classification

# Get clusters and linkage matrix Z
clusters_h, Z = get_hca_clusters(returns_df,k=k)


# Plot Dendogram chart
plt.figure(figsize=(18,8))
dendrogram(Z)
plt.title(f'Dendrogram of {returns_df.shape[1]} sampled stocks')
plt.xlabel('Stocks')
plt.ylabel('Distance')
plt.show()


# Sort stocks based on HCA leaves (Dendogram level 0)
stocks_names_HCA_sorted = returns_df.T.iloc[leaves_list(Z)].T.columns

# Sort stocks by GICS Sectors
GICS_sorted = returns_df.T.join(data['GICS Sector']).sort_values('GICS Sector')


# Plot Correlation Heatmaps
X = returns_df.copy()

fig = make_subplots(rows=2, cols=2, subplot_titles=('Unclustered Stocks', 
                                                    f'GICS Sectors',
                                                    f'PCA & K-Means Clustering',
                                                   'Hierarchical Clustering',
                   ))

heatmap1 = px.imshow(X.corr())
heatmap2 = px.imshow(X[GICS_sorted.index].corr())
heatmap3 = px.imshow(X[clusters_k.index].corr())
heatmap4 = px.imshow(X[stocks_names_HCA_sorted].corr())


fig.add_trace(heatmap1.data[0], row=1, col=1)
fig.add_trace(heatmap2.data[0], row=1, col=2)
fig.add_trace(heatmap3.data[0], row=2, col=1)
fig.add_trace(heatmap4.data[0], row=2, col=2)

fig.update_layout(height=1000, 
                  width=900, 
                  showlegend=True,
                  coloraxis={'colorscale': 'viridis'},
                 title='Correlation Heatmaps Comparison')

fig.show()


# PCA-K-Means clustering details
clusters = clusters_k

df = clusters.join(data)
KMEAN_ret = returns_df.T.join(df).groupby('cluster').mean().T
grouped = df.groupby(['cluster', 'GICS Sector', 'Security']).size().reset_index(name='count')

fig = px.bar(grouped, x='cluster', y='count', color='GICS Sector', title=f'PCA & K-Means clustering',
             barmode='stack',hover_data=['Security'],text='Security',
            height=800,
            width=1400)

fig.update_layout(xaxis_title='Cluster', yaxis_title='Security count', hovermode='closest')
fig.show()


# Within-cluster correlation
df = clusters_k.join(data)
within_kmean_corr = []
for c in set(df.cluster.values):
    temp = returns_df.T.join(df)
    temp = temp[temp.cluster == c].T
    temp = temp[:-4]
    temp = temp.astype(float)
    corr_mat = temp.corr()
    upper = np.triu(corr_mat,k=1)
    corr_mean = np.mean(upper[upper!=0])
    if not np.isnan(corr_mean):
        within_kmean_corr.append(corr_mean)
within_corr_mean = np.mean(within_kmean_corr)

# Between-cluster correlation
corr_mat = KMEAN_ret.corr()
upper = np.triu(corr_mat,k=1)
between_corr_mean = np.mean(upper[upper!=0])

corr_comp_df = pd.DataFrame([within_corr_mean,between_corr_mean],index=['Within Corr','Between Corr'],columns=['PCA-KMEANS'])
corr_comp_df


# HCA Clustering details
clusters = clusters_h

df = clusters.join(data)
HCA_ret = returns_df.T.join(df).groupby('cluster').mean().T
grouped = df.groupby(['cluster', 'GICS Sector', 'Security']).size().reset_index(name='count')

fig = px.bar(grouped, x='cluster', y='count', color='GICS Sector', title=f'Hierarchical clustering',
             barmode='stack',hover_data=['Security'],text='Security',
            height=800,
            width=1400)

fig.update_layout(xaxis_title='Cluster', yaxis_title='Security count', hovermode='closest')
fig.show()


# Within-cluster correlation
df = clusters_h.join(data)
within_hca_corr = []
for c in set(df.cluster.values):
    temp = returns_df.T.join(df)
    temp = temp[temp.cluster == c].T
    temp = temp[:-4]
    temp = temp.astype(float)
    corr_mat = temp.corr()
    upper = np.triu(corr_mat,k=1)
    corr_mean = np.nanmean(upper[upper!=0])
    if not np.isnan(corr_mean):
        within_hca_corr.append(corr_mean)
within_corr_mean = np.mean(within_hca_corr)

# Between-cluster correlation
corr_mat = HCA_ret.corr()
upper = np.triu(corr_mat,k=1)
between_corr_mean = np.mean(upper[upper!=0])

corr_comp_df['HCA'] = [within_corr_mean,between_corr_mean]
corr_comp_df

/var/folders/sr/2_q1kwss0cg7rt_ny655psg80000gn/T/ipykernel_8565/1808345271.py:11: RuntimeWarning:

Mean of empty slice


# GICS Clustering details
clusters = returns_df.T

df = clusters.join(data)
GICS_ret = df.groupby('GICS Sector').mean().T
grouped = df.groupby(['GICS Sector', 'Security']).size().reset_index(name='count')

fig = px.bar(grouped, x='GICS Sector', y='count', color='GICS Sector', title=f'GICS Sectors clustering',
             barmode='stack',hover_data=['Security'],text='Security',
            height=800,
            width=1400)

fig.update_layout(xaxis_title='Cluster', yaxis_title='Security count', hovermode='closest')
fig.show()


# Within-cluster correlation
df = returns_df.T.join(data)
within_GICS_corr = []
sector = np.unique(df['GICS Sector'].values)
for c in sector:
    temp = df.copy()
    temp = temp[temp['GICS Sector'] == c].T
    temp = temp[:-4]
    temp = temp.astype(float)
    corr_mat = temp.corr()
    upper = np.triu(corr_mat,k=1)
    corr_mean = np.nanmean(upper[upper!=0])
    if not np.isnan(corr_mean):
        within_GICS_corr.append(corr_mean)
within_corr_mean = np.mean(within_GICS_corr)

# Between-cluster correlation
corr_mat = GICS_ret.corr()
upper = np.triu(corr_mat,k=1)
between_corr_mean = np.mean(upper[upper!=0])

corr_comp_df['GICS'] = [within_corr_mean,between_corr_mean]
corr_comp_df


low = 2
high = 50
step = 1

# Calculate silhouette scores for different values of k
from sklearn.metrics import silhouette_score
silhouette_scores = []
sse=[]
W,_,_,_= train_PCA(returns_df,n_comp=20)


for i in range(low,high,step):
    kmeans = KMeans(n_clusters=i)
    kmeans.fit(W)
    labels = kmeans.labels_
    # Assign stocks to clusters
    clusters_k = pd.DataFrame(labels,index=W.index,columns=['cluster'])
    clusters_k = clusters_k.sort_values(by='cluster')
    
    silhouette_avg = silhouette_score(returns_df.T,labels)
    silhouette_scores.append(silhouette_avg) # silhouette
    sse.append(kmeans.inertia_) # within-cluster sse

Total explained variance:0.67 with 20 PCs


# Plot the silhouette scores
plt.plot(range(low,high,step),silhouette_scores,marker='o')
plt.xlabel('Number of clusters')
plt.ylabel('Silhouette score')
plt.show()


# Plot within cluster sum of squares
plt.plot(range(low,high,step),sse,marker='o')
plt.xlabel('Number of clusters')
plt.ylabel('Within-cluster sse')
plt.show()

	Security	GICS Sector	GICS Sub-Industry
Symbol
IPG	Interpublic Group of Companies (The)	Communication Services	Advertising
OMC	Omnicom Group	Communication Services	Advertising
WBD	Warner Bros. Discovery	Communication Services	Broadcasting
CHTR	Charter Communications	Communication Services	Cable & Satellite
CMCSA	Comcast	Communication Services	Cable & Satellite

	A	AAL	AAP	AAPL	ABBV	ABC	ABT	ACGL	ACN	ADBE	...	WYNN	XEL	XOM	XRAY	XYL	YUM	ZBH	ZBRA	ZION	ZTS
Date
2014-12-31	38.084969	50.814606	147.124634	24.767366	45.798306	78.874535	38.343548	19.700001	77.527657	72.699997	...	130.989746	27.941647	62.913483	49.859367	34.242157	44.820728	103.148308	77.410004	23.585787	40.600727
2015-01-01	38.084969	50.814606	147.124634	24.767366	45.798306	78.874535	38.343548	19.700001	77.527657	72.699997	...	130.989746	27.941647	62.913483	49.859367	34.242157	44.820728	103.148308	77.410004	23.585787	40.600727
2015-01-02	37.823860	51.079906	146.459518	24.531763	46.113235	79.136978	38.241344	19.496668	77.119682	72.339996	...	129.343124	28.097225	63.172108	48.605175	34.251160	44.513115	102.393486	77.430000	23.403790	40.864925
2015-01-03	37.823860	51.079906	146.459518	24.531763	46.113235	79.136978	38.241344	19.496668	77.119682	72.339996	...	129.343124	28.097225	63.172108	48.605175	34.251160	44.513115	102.393486	77.430000	23.403790	40.864925
2015-01-04	37.823860	51.079906	146.459518	24.531763	46.113235	79.136978	38.241344	19.496668	77.119682	72.339996	...	129.343124	28.097225	63.172108	48.605175	34.251160	44.513115	102.393486	77.430000	23.403790	40.864925

	A	AAL	AAP	AAPL	ABBV	ABC	ABT	ACGL	ACN	ADBE	...	WYNN	XEL	XOM	XRAY	XYL	YUM	ZBH	ZBRA	ZION	ZTS
Date
2015-01-11	0.000740	-0.035058	0.010974	0.024513	-0.001669	0.028079	0.006681	0.010600	0.010581	-0.006912	...	0.014705	0.001661	-0.007864	0.015983	-0.071166	0.015342	0.049915	0.040165	-0.078827	0.021704
2015-01-18	-0.057650	-0.042484	-0.064254	-0.053745	-0.011485	-0.006237	-0.010498	0.002368	-0.009913	-0.001531	...	-0.013821	0.023217	-0.010640	-0.037907	-0.025445	-0.008422	-0.010236	0.029426	-0.049117	-0.000678
2015-01-25	0.014641	0.118049	0.038534	0.065950	-0.032693	0.024995	-0.014161	0.002700	0.003713	0.032483	...	-0.006667	0.019990	-0.002525	0.002561	0.020308	0.023195	-0.000171	0.015438	0.001211	-0.000385

	PEG	XYL	HSY	ILMN	VZ	ADSK	PAYX	ISRG	WFC	NTAP	...	BWA	PCG	PNC	SNA	CPRT	AMP	XOM	CAG	PEP	SHW
Date
2015-01-11	-0.013604	-0.071166	0.026034	0.050588	0.007521	-0.021166	0.019464	-0.008943	-0.036928	-0.015444	...	-0.022287	0.046682	-0.044593	-0.004109	-0.012575	-0.033386	-0.007864	0.011725	0.025201	0.045649
2015-01-18	0.053714	-0.025445	0.039940	-0.056365	0.026305	-0.024369	0.003394	0.018738	-0.019742	-0.046740	...	-0.050822	0.041734	-0.021401	-0.023355	-0.030731	-0.023653	-0.010640	-0.000276	0.004854	-0.002187
2015-01-25	0.010333	0.020308	-0.018435	0.072571	-0.017504	0.023571	0.022833	-0.024612	0.031371	0.018839	...	0.078346	0.012208	0.021791	0.013428	0.053985	0.038665	-0.002525	0.014628	0.012745	0.000694

	PCA-KMEANS	HCA	GICS
Within Corr	0.525310	0.519254	0.506066
Between Corr	0.656626	0.590020	0.687749

Unsupervised Learning for stocks clustering (PCA K-MEANS HCA)¶

Imports¶

Data Preparation¶

Loading tickers¶

Collecting Prices¶

Computing Returns¶

Random Sample¶

Principle Component Analysis (PCA)¶

K-Means Clustering¶

Run K-Means¶

HCA - Hierachical Cluster Analysis¶

Correlation Matrices - Clustering methods comparison¶

Clustering details by stock & sector / within & between correlation assessment¶

APPENDIX: Optimal k number of clusters (silhouette, within cluster distance)¶

Thanks for reading !¶